Investment Strategies: Efficient Diversification

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Questions and Answers

What does the Efficient Frontier represent in the context of risky assets?

A set of portfolios that maximizes expected return for a given level of risk (correct)

The minimum risk for any portfolio return

The relationship between risk-free assets and risky assets

The average risk of a portfolio

Which of the following methods is NOT used to determine the Efficient Frontier?

Maximize stock price growth (correct)

Maximize risk premium for any level standard deviation

Maximize Sharpe ratio for any standard deviation or risk premium

Minimize standard deviation for any level risk premium

What is the role of the Separation Property in portfolio management?

To separate portfolio choice into two tasks (correct)

To determine the risk-free rate accurately

To guarantee maximum returns irrespective of risk

To create a continuous line of asset allocation

What is the optimal risky portfolio's position relative to the Efficient Frontier?

It is tangent to the Efficient Frontier Signup and view all the answers

Which strategy involves minimizing the standard deviation for a given level of risk premium?

Efficient diversification Signup and view all the answers

Which of the following statements about the Efficient Frontier is true?

It helps investors choose portfolios based on their risk-return profile Signup and view all the answers

Which option correctly identifies the tasks involved in portfolio selection according to the Separation Property?

Determining the optimal risky portfolio and personal asset mix Signup and view all the answers

Which of the following options is NOT associated with maximizing the Sharpe ratio?

Focusing on absolute returns irrespective of volatility Signup and view all the answers

What is the main focus when evaluating risk for asset allocation using historical data?

Deviations of returns from average value Signup and view all the answers

What does the slope of the Capital Allocation Line (CAL) represent?

The Sharpe Ratio of the risky portfolio Signup and view all the answers

Which of the following formulas is used to calculate the weight of the first risky asset in an optimal risky portfolio?

wB = [ E (rB ) - rf ]σS^2 - [ E (rs ) - rf ]σBσSρBS Signup and view all the answers

In the context of asset allocation, what does the term 'optimal risky portfolio' refer to?

The best combination of risky and safe assets Signup and view all the answers

What do historical data analysis reveal about the variability and covariability of asset returns?

They change slowly over time and can be predicted with accuracy. Signup and view all the answers

Which variable is NOT included in the calculation of the weight of a risky asset in the optimal portfolio formula?

Market capitalization of the asset Signup and view all the answers

What does the ratio $ ho$ represent in the context of systematic variance?

The ratio of systematic variance to total variance Signup and view all the answers

When estimating the averages of asset returns using historical data, which of the following limitations is present?

Estimates may not be precise due to sample bias. Signup and view all the answers

In the equation $eta rac{ au^2_D}{ au^2_M} = rac{ au^2_D}{ au^2_M}$, which variable corresponds to the total variance of the stock?

$ au^2_D$ Signup and view all the answers

The optimal allocation in a portfolio involving bonds, stocks, and T-bills aims for what outcome?

A balance between risk and return Signup and view all the answers

Which equation is used to express the systematic variance in the context of stocks?

$ au^2_D = eta au^2_M + au^2(e_D)$ Signup and view all the answers

What is the primary purpose of the optimal risky portfolio discussed in efficient diversification?

To create a globally diversified portfolio Signup and view all the answers

What is the main purpose of a scatter diagram in analyzing stock data?

To illustrate the relationship between two variables Signup and view all the answers

What does $eta$ in a single-index model relate to?

The systematic risk of the stock compared to the market Signup and view all the answers

Which of the following best defines beta in a single-index stock market model?

The sensitivity of a security’s returns to market movements Signup and view all the answers

What type of risk can be eliminated through diversification?

Firm-specific risk Signup and view all the answers

What does alpha represent in the context of a stock's performance?

The expected return beyond market influences Signup and view all the answers

Which component is NOT part of the excess return in a single-index stock market model?

Fundamental analysis of the stock Signup and view all the answers

What does portfolio risk primarily depend on when considering two assets?

The covariance between the returns of the assets Signup and view all the answers

Which formula represents the expected return on a two-security portfolio?

E(r) = W1r1 + W2r2 Signup and view all the answers

What does the Security Characteristic Line (SCL) represent?

The plot of predicted excess return against market excess return Signup and view all the answers

Which risk factors are considered nonsystematic?

Risks unique to individual companies Signup and view all the answers

What does firm-specific or residual risk refer to?

Component of return variance independent of market factors Signup and view all the answers

How is the expected excess return of a stock calculated in the single-index model?

Considering both market influences and firm-specific events Signup and view all the answers

What is the primary characteristic of market risk?

It affects all securities in the market Signup and view all the answers

What do the terms W1 and W2 represent in the expected return formula for a portfolio?

Proportion of funds invested in each security Signup and view all the answers

Which factor is NOT included in the calculation of total return for a financial asset?

Market volatility Signup and view all the answers

What is the effect of increasing the number of stocks in a portfolio on risk?

Risk decreases but at a diminishing rate Signup and view all the answers

Which of the following is classified as systematic risk?

Risk associated with interest rate changes Signup and view all the answers

What does the equation for nonsystematic portion of portfolio return represent?

The weighted return of individual securities Signup and view all the answers

How is the portfolio nonsystematic variance computed?

By summing the squares of the weights multiplied by the securities' variances Signup and view all the answers

What does the information ratio measure?

The ratio of alpha to the standard deviation of residual Signup and view all the answers

What is an active portfolio?

A portfolio formed by optimally combining analyzed stocks Signup and view all the answers

Which component is NOT part of nonsystematic risk in a portfolio?

Market shifts impacting all securities Signup and view all the answers

In a portfolio of n securities, what does 'wi' represent?

The weight of a specific security within the portfolio Signup and view all the answers

What primarily differentiates nonsystematic risk from systematic risk?

Nonsystematic risk is avoidable through diversification Signup and view all the answers

Which statement about portfolio return calculations is accurate?

Nonsystematic return contributes to overall portfolio return Signup and view all the answers

Study Notes

Chapter 6: Efficient Diversification

This chapter covers efficient diversification, a crucial investment strategy.
Efficient Diversification is a method of reducing risk by investing in a variety of assets.

6.1 Diversification and Portfolio Risk

Market, Systematic, & Nondiversifiable Risk: Risk factors affecting the entire economy, cannot be removed.
Unique, Firm-Specific, Nonsystematic & Diversifiable Risk: Risk particular to a specific company, which can be mitigated through diversification.

Figure 6.1 Risk as Function of Number of Stocks in Portfolio

As the number of stocks in a portfolio increases, the diversifiable risk declines.
The risk of firms, unique to each firm, decreases as the portfolio grows.
Market risk remains constant, even with a larger portfolio.

Figure 6.2 Risk Versus Diversification

Portfolio risk decreases substantially as the number of stocks in the portfolio increases, becoming relatively stable after a certain number of stocks.

Spreadsheet 6.1 Capital Market Expectations

This spreadsheet shows projected rates of return for stock and bond funds in various economic scenarios.
The likelihood and effect of each economic scenario is outlined.

6.2 Asset Allocation with Two Risky Assets

Covariance and Correlation: The relationship between the returns of assets; portfolio risk depends on the covariance between asset returns.
Expected return on two-security portfolio: The anticipated return of a portfolio comprising two securities, dependent on weights and returns of individual securities.

Spreadsheet 6.2 Variance & Standard Deviations of Returns

This details calculations of variance and standard deviation of returns across various economic scenarios for stock and bond funds.
The spreadsheet shows various scenarios and the deviation from the expected return.

Spreadsheet 6.3 Portfolio Performance

This spreadsheet shows how a portfolio comprised of 40% stock and 60% bond funds performs in various economic scenarios.

Spreadsheet 6.4 Return Covariance

This spreadsheet calculates the covariance between the returns of stock and bond funds in various economic scenarios.

6.2 Asset Allocation with Two Risky Assets: Covariance and Correlation

Portfolio Risk: Depends on the covariance of asset returns.
Expected Return Formula: E(rp) = W₁r₁ + W₂r₂ (where W₁ and W₂ are weights, r₁ and r₂ are returns).

Spreadsheet 6.6 Opportunity Set – Various Correlation Coefficients

Calculates portfolio expected returns (E(rp)).
Calculates portfolio standard deviation (σp).

Figure 6.3 Investment Opportunity Set

Illustrates the trade-off between risk and return for various portfolios.
The efficient frontier displays portfolios with the highest possible expected returns for a given level of risk.

Figure 6.4 Opportunity Sets: Various Correlation Coefficients

Shows how the shape of the efficient frontier changes depending on the correlation between assets.

6.2 Asset Allocation with Two Risky Assets: RoR, ERR, and Variance

RoR (Return on Risk): Weighted average of returns on components. Provides weights dependent on investment proportions.
ERR (Expected Return on Risk): Weighted average of expected returns with proportions as weights. Provides portfolio proportions to calculate weights.
Variance of RoR: σ₂ = (ω₂σ₂)² + (ω₂σ₂)² + 2(ω₁σ₁)(ω₂σ₂)ρ₁₂

6.2 Asset Allocation with Two Risky Assets: Mean-Variance Criterion

Portfolio Dominance: Portfolio A dominates Portfolio B if E(r₁) ≥ E(r₂) and σ₁ ≤ σ₂

6.4 Efficient Diversification with Many Risky Assets -Choosing Optimal Risky Portfolio

Efficient Frontier of Risky Assets: A graph illustrating which portfolios maximize expected return at each level of portfolio risk
Separation Property: Allows the choice of the optimal portfolio to be divided into two tasks.
Optimal Risky Portfolio: The optimal-risk portfolio is determined by maximizing the Sharpe ratio.

6.4 Efficient Diversification with Many Risky Assets -Optimal Risky Portfolio: Illustration

Illustrates the construction of a global portfolio using stock market indices.
Emphasizes that risk premiums are forecast by fundamental analysis.

6.4 Efficient Diversification with Many Risky Assets - Using Historical Data

Variability/covariability is assumed to be somewhat stable over time, enabling estimation using historical data.
Realized returns are used to accurately estimate average returns.
Focus is put on returns from the average value, due to difficulty in precisely estimating the averages.

Figure 6.11 Efficient Frontiers & CAL: Table 6.1

Presents a table highlighting risk premium versus standard deviation, comparing various portfolios (with and without short sales).

6.5 A Single-Index Stock Market

Index Model: Links stock returns to broad market returns and firm-specific factors.
Excess Return: Return in excess of the risk-free rate.
Beta: Measures a security's sensitivity to market factor.
Firm-Specific Risk: Variance independent of the market factor.
Alpha: A stock's expected return beyond the amount induced by the market index.

6.5 A Single-Index Stock Market: Statistical and Graphical Representation

Security Characteristic Line (SCL): Displays a security's anticipated excess return relative to market excess return.
Systematic Variance (β²): The proportion of total variance attributed to movements in the overall market.
Formula: β² = σ²DM / σ²D

Figure 6.12 Scatter Diagram for U.S. Steel

Shows a scatter diagram for U.S. Steel and a regression line which helps to identify the overall market trends.

Figure 6.13 Various Scatter Diagrams

Shows eight scatter diagrams of various securities with the market index.

6.5 A Single-Index Stock Market: Diversification

Diversification in Single-Index Security Market: The diversification of a portfolio of n securities using their respective weights in the portfolio.
Portfolio Nonsystematic Variance: The variance of a portfolio's nonsystematic return component.
Formula: σ²ₑₚ = ∑ᵢ=₁ⁿ wᵢ²σ²ₑᵢ

6.5 A Single-Index Stock Market -Using Security Analysis

Information ratio - The ratio of active portfolio alpha to its standard deviation of residual.
Active portfolio: Portfolio formed by the optimal combination of analyzed stocks.

6.6 Risk of Long-Term Investments

Why the Unending Confusion: The majority of financial advisors believe stock risk decreases with longer investment stretches.
Longer horizons lead to increasing risk premium and variance, while Sharpe ratios still grow dependent on the horizon.

Table 6.4 Investment Risk for Different Horizons

This lists investment risk for various time horizons.

6.7 The Optimal Risky Portfolio with a Risk-Free Asset

Sharpe Ratio: A measure of risk-adjusted return to assess the potential of CAL to generate optimal return.

6.7 The Optimal Risky Portfolio with a Risk-Free Asset: Calculating Optimal Risky Portfolio

Formulae for calculating portfolio weights (W and W) are displayed, and optimal portfolios are linked with Cal.

Figure 6.5 Two Capital Allocation Lines

Shows the CAL relative to other portfolios, outlining the various possible mixes of risky and risk-free assets.

Figure 6.6 Bond, Stock, and T-Bill Optimal Allocation

Illustrates the graphical approach of choosing the optimal portfolio, based on various allocation possibilities of risky assets.

Figure 6.7 The Complete Portfolio

Shows portfolios with increasing risk and expected returns in a risk-return graph.

Figure 6.8 Portfolio Composition: Asset Allocation Solution

Visually displays the portfolio composition of stock, bonds, and T-bills for a specific portfolio (labeled as Portfolio O).

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Description

Explore the principles of efficient diversification in investments with a focus on portfolio risk factors. This quiz discusses market, systematic, and unique risks, as well as the impact of increasing stock numbers on risk reduction. Test your knowledge on methods to mitigate investment risks through diversification.